When serious work needs to be done with radicals,
they are usually changed to a name that uses exponents,
so that the exponent laws can be used.
Also, this new name for radicals allows them to be approximated on any calculator that has a power key.

Regardless of the name used, the normal restrictions apply.
For example,
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$\,x^{1/2}\,$ is only
defined for
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$\,x\ge 0\,$.